Circular railway

The railway connects in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track be from A to C?

Correct answer:

b1 =  103.1095 km

Step-by-step explanation:

c=30 km b=95 km a=70 km  s=2a+b+c=270+95+30=2195=97.5 km S=s (sa) (sb) (sc)=97.5 (97.570) (97.595) (97.530)672.6522 km2  r=S/s=S/2195=672.6522/97.56.899 km  R=4 r sa b c=4 r 2195a b c=4 6.899 97.570 95 3074.1468 km  ΔRRb b2=R2+R22 R2 cosθ  θ=arccos(2 R22 R2b2)=arccos(2 74.146822 74.14682952)1.3906 rad  b1=θ R=1.3906 74.1468=103.1095 km

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